Question

the midpoint of $overline{ab}$ is $m=(6,4)$. one endpoint is $a=(8,6)$. find the coordinates of the other endpoint, $b$.

Explanation:

Step1: Recall mid - point formula

The mid - point formula for two points \(A(x_1,y_1)\) and \(B(x_2,y_2)\) is \(M(\frac{x_1 + x_2}{2},\frac{y_1 + y_2}{2})\). Here \(A=(8,6)\), \(M=(6,4)\), and \(B=(x,y)\).

Step2: Solve for \(x\)

We know that \(\frac{8 + x}{2}=6\). Multiply both sides by 2: \(8 + x=12\). Then subtract 8 from both sides: \(x=12 - 8=4\).

Step3: Solve for \(y\)

We know that \(\frac{6 + y}{2}=4\). Multiply both sides by 2: \(6 + y=8\). Then subtract 6 from both sides: \(y=8 - 6 = 2\).

Answer:

\((4,2)\)